{"as_of":"2026-08-20T05:16:00Z","caps":{"database_statements":6,"inbound":100,"outbound":100},"context_digest":"sha256:715859575737606c828a48c13b0ef98c165a0abb9c0c4129548b7c284ec71bcb","coverage":[{"denominator":50,"lane":"reference_resolution","note":"Typed states for the displayed outbound observations.","records_observed":50,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-06T20:44:22.212392Z","state":"measured"},{"denominator":64,"lane":"standing_notices","note":"One-hop event checks from named stored sources.","records_observed":64,"source":"scholarly_work_events, retraction_status_cache","source_observed_at":"2026-08-19T06:32:44.657259+00:00","state":"measured"},{"denominator":14,"lane":"inbound_itemization","note":"Pith citing papers itemized under the disclosed page cap.","records_observed":14,"source":"paper_references, paper_reference_links","source_observed_at":"2026-08-15T17:27:52.900010Z","state":"measured"},{"denominator":1,"lane":"external_citation_measurements","note":"A source-named dated measurement, never combined with another source.","records_observed":0,"source":"pith","source_observed_at":"2026-07-10T08:26:58.960977Z","state":"measured"}],"external_citation_measurements":[],"inbound":[{"citation":{"cited_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.02375","snapshot_observed_at":"2026-08-06T17:05:58.021135Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.11951","last_updated":"2025-07-16T06:35:07Z","snapshot_observed_at":"2026-08-15T06:22:55.495332Z","submitted_at":"2025-07-16T06:35:07Z","title":"A radiative lepton model in a non-invertible fusion rule","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T17:05:58.021135Z"},"links":{"cited_paper":"/paper/2507.02375","citing_paper":"/paper/2507.11951"},"observation_digest":"sha256:cd1bf8959d1e378e0bde2ea4097bb3d9a187ecbac82557f4abc1b78be1f2a347","observation_id":"e69d90ef-93e9-4517-9986-e89524e024d9","resolution":{"observed_at":"2026-08-06T17:05:58.021135Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.02375","snapshot_observed_at":"2026-08-06T15:27:52.529010Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.16198","last_updated":"2025-07-22T03:19:16Z","snapshot_observed_at":"2026-08-14T19:48:26.568275Z","submitted_at":"2025-07-22T03:19:16Z","title":"Three-loop induced neutrino mass model in a non-invertible symmetry","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T15:27:52.529010Z"},"links":{"cited_paper":"/paper/2507.02375","citing_paper":"/paper/2507.16198"},"observation_digest":"sha256:a3febf66dbe676022d16a7c031b7e10589fe99d66b9e2242f21251a3dcf2706e","observation_id":"e3acbff9-d5e3-4285-ad97-e40ca1c76c3c","resolution":{"observed_at":"2026-08-06T15:27:52.529010Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.02375","snapshot_observed_at":"2026-08-15T17:27:52.900010Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2508.12287","last_updated":"2025-08-17T08:34:18Z","snapshot_observed_at":"2026-08-16T21:57:45.276805Z","submitted_at":"2025-08-17T08:34:18Z","title":"Non-invertible Symmetry as a Solution to the Strong CP Problem in a GUT-inspired Standard Model","version":1},"reference_index":38,"source":"arxiv_source","source_observed_at":"2026-08-15T17:27:52.900010Z"},"links":{"cited_paper":"/paper/2507.02375","citing_paper":"/paper/2508.12287"},"observation_digest":"sha256:fcf1a85ab63e835dce90195e9583ad7765a47def717910c12b21590e0fe6250d","observation_id":"4ca244aa-95f2-44e2-9f30-efc41a6a863b","resolution":{"observed_at":"2026-08-15T17:27:52.900010Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"cited_work":{"arxiv_id":"2507.02375","doi":null,"metadata_source":"pith","pith_arxiv_id":"2507.02375","snapshot_observed_at":"2026-07-10T08:26:58.960977Z","title":"On discrete gauging and non-invertible selection rules","venue":"hep-th","work_id":"221f546f-a826-47a7-b2a5-a7bdc63284e6","year":2025},"citing_paper":{"arxiv_id":"2508.14970","last_updated":"2026-04-23T09:45:55Z","snapshot_observed_at":"2026-08-11T01:12:43.317371Z","submitted_at":"2025-08-20T18:00:03Z","title":"Spurion Analysis for Non-Invertible Selection Rules from Near-Group Fusions","version":2},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-05-18T22:06:51.905581Z"},"links":{"cited_paper":"/paper/2507.02375","citing_paper":"/paper/2508.14970"},"observation_digest":"sha256:482193b08a676f26387cfbc7a6a2235fd8b73043c34c5035b41ac3618877a0e2","observation_id":"425d2c78-95df-46f1-9046-66bbe08791d0","resolution":{"observed_at":"2026-05-18T22:11:53.150792Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.02375","snapshot_observed_at":"2026-08-05T17:29:38.018663Z","title":"Dong , author T","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2508.16174","last_updated":"2025-08-22T07:51:19Z","snapshot_observed_at":"2026-08-18T01:09:24.595403Z","submitted_at":"2025-08-22T07:51:19Z","title":"A natural realization of inverse seesaw model in a non-invertible selection rule","version":1},"reference_index":27,"source":"arxiv_source","source_observed_at":"2026-08-05T17:29:38.018663Z"},"links":{"cited_paper":"/paper/2507.02375","citing_paper":"/paper/2508.16174"},"observation_digest":"sha256:3c400fa4c01e697a53746e1d432b72d02354a4da4b263c9e772d7e1c48ff1f7c","observation_id":"3ca456d3-1d99-421a-8d9d-d3ae3e598ded","resolution":{"observed_at":"2026-08-05T17:29:38.018663Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.02375","snapshot_observed_at":"2026-08-04T18:31:50.241367Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2509.10019","last_updated":"2025-09-12T07:23:04Z","snapshot_observed_at":"2026-08-17T15:30:14.277098Z","submitted_at":"2025-09-12T07:23:04Z","title":"Non-Invertible Selection Rules on Heterotic Non-Abelian Orbifolds","version":1},"reference_index":66,"source":"pdf_text","source_observed_at":"2026-08-04T18:31:50.241367Z"},"links":{"cited_paper":"/paper/2507.02375","citing_paper":"/paper/2509.10019"},"observation_digest":"sha256:d572b7acfeaf437e9d19505df4a3bc804534e85d24da5db42edd59afc72aee0a","observation_id":"c89b5013-dd55-4fa7-acee-522536b9e153","resolution":{"observed_at":"2026-08-04T18:31:50.241367Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2507.02375","snapshot_observed_at":"2026-08-04T09:11:28.833215Z","title":null,"venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2510.17156","last_updated":"2026-06-16T22:51:07Z","snapshot_observed_at":"2026-08-17T06:21:45.647984Z","submitted_at":"2025-10-20T04:57:05Z","title":"Radiative lepton model in a non-invertible fusion rule","version":2},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-04T09:11:28.833215Z"},"links":{"cited_paper":"/paper/2507.02375","citing_paper":"/paper/2510.17156"},"observation_digest":"sha256:af09ec0c16bf77362cbcebc6454c950648cf7f73ce59ba30260b455b90bdfb31","observation_id":"177a0076-18eb-49b7-95a4-6dab7aeb42dc","resolution":{"observed_at":"2026-08-04T09:11:28.833215Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"cited_work":{"arxiv_id":"2507.02375","doi":null,"metadata_source":"pith","pith_arxiv_id":"2507.02375","snapshot_observed_at":"2026-07-10T08:26:58.960977Z","title":"On discrete gauging and non-invertible selection rules","venue":"hep-th","work_id":"221f546f-a826-47a7-b2a5-a7bdc63284e6","year":2025},"citing_paper":{"arxiv_id":"2511.00386","last_updated":"2026-05-19T13:08:03Z","snapshot_observed_at":"2026-08-16T12:20:22.222148Z","submitted_at":"2025-11-01T03:39:10Z","title":"Conformal Bootstrap with Duality-Inspired Fusion Rule","version":2},"reference_index":88,"source":"pdf_text","source_observed_at":"2026-05-21T19:45:34.507657Z"},"links":{"cited_paper":"/paper/2507.02375","citing_paper":"/paper/2511.00386"},"observation_digest":"sha256:47915e9cf3082854e7b84bd4a103cfad8e34ba17b8ec97c0541481375d782d08","observation_id":"fd5bb8a5-b068-43cd-aaad-4e9731e49ad0","resolution":{"observed_at":"2026-05-21T19:50:33.922515Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"cited_work":{"arxiv_id":"2507.02375","doi":null,"metadata_source":"pith","pith_arxiv_id":"2507.02375","snapshot_observed_at":"2026-07-10T08:26:58.960977Z","title":"On discrete gauging and non-invertible selection rules","venue":"hep-th","work_id":"221f546f-a826-47a7-b2a5-a7bdc63284e6","year":2025},"citing_paper":{"arxiv_id":"2604.04423","last_updated":"2026-04-06T05:02:37Z","snapshot_observed_at":"2026-08-16T19:34:10.550171Z","submitted_at":"2026-04-06T05:02:37Z","title":"Dynamical CP Violation from Non-Invertible Selection Rules","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-05-10T19:53:38.648044Z"},"links":{"cited_paper":"/paper/2507.02375","citing_paper":"/paper/2604.04423"},"observation_digest":"sha256:14fd35fb69753291556992557176034085c03389925d2790dec0901195b0b778","observation_id":"e5025f7b-adc2-4d90-8556-e51c5dc4c0c8","resolution":{"observed_at":"2026-05-10T22:25:50.744772Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"cited_work":{"arxiv_id":"2507.02375","doi":null,"metadata_source":"pith","pith_arxiv_id":"2507.02375","snapshot_observed_at":"2026-07-10T08:26:58.960977Z","title":"On discrete gauging and non-invertible selection rules","venue":"hep-th","work_id":"221f546f-a826-47a7-b2a5-a7bdc63284e6","year":2025},"citing_paper":{"arxiv_id":"2604.09345","last_updated":"2026-04-10T14:17:02Z","snapshot_observed_at":"2026-08-11T20:03:05.778491Z","submitted_at":"2026-04-10T14:17:02Z","title":"A General Prescription for Spurion Analysis of Non-Invertible Selection Rules","version":1},"reference_index":56,"source":"pdf_text","source_observed_at":"2026-05-10T17:24:03.346127Z"},"links":{"cited_paper":"/paper/2507.02375","citing_paper":"/paper/2604.09345"},"observation_digest":"sha256:a90b2e1955fa741bf28d52982c779ca8ce040767a75ddb4a1709e856b3871156","observation_id":"f4174b1d-15a5-4936-bd18-b0b9070cb87c","resolution":{"observed_at":"2026-05-11T06:51:53.514238Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"cited_work":{"arxiv_id":"2507.02375","doi":null,"metadata_source":"pith","pith_arxiv_id":"2507.02375","snapshot_observed_at":"2026-07-10T08:26:58.960977Z","title":"On discrete gauging and non-invertible selection rules","venue":"hep-th","work_id":"221f546f-a826-47a7-b2a5-a7bdc63284e6","year":2025},"citing_paper":{"arxiv_id":"2604.11308","last_updated":"2026-04-13T11:08:34Z","snapshot_observed_at":"2026-08-17T09:57:43.808481Z","submitted_at":"2026-04-13T11:08:34Z","title":"Dirac one-loop seesaw in a non-invertible fusion rule","version":1},"reference_index":84,"source":"pdf_text","source_observed_at":"2026-05-10T16:32:37.745450Z"},"links":{"cited_paper":"/paper/2507.02375","citing_paper":"/paper/2604.11308"},"observation_digest":"sha256:a6bd84824062d6e9b4a520df69a2d559220e19b9d8a044ad4fc9d02d8eedd8d3","observation_id":"4b846ea5-c226-4ea4-9c84-0e6ba5069eeb","resolution":{"observed_at":"2026-05-11T08:41:00.583570Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"cited_work":{"arxiv_id":"2507.02375","doi":null,"metadata_source":"pith","pith_arxiv_id":"2507.02375","snapshot_observed_at":"2026-07-10T08:26:58.960977Z","title":"On discrete gauging and non-invertible selection rules","venue":"hep-th","work_id":"221f546f-a826-47a7-b2a5-a7bdc63284e6","year":2025},"citing_paper":{"arxiv_id":"2605.23202","last_updated":"2026-05-22T03:36:44Z","snapshot_observed_at":"2026-08-15T04:57:04.883090Z","submitted_at":"2026-05-22T03:36:44Z","title":"Zee models with a non-invertible $Z_M$ symmetry","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-05-25T04:32:47.321869Z"},"links":{"cited_paper":"/paper/2507.02375","citing_paper":"/paper/2605.23202"},"observation_digest":"sha256:1359b1b57605fbf0284a96c7de5ba9b574f77073d318c420bed91a4fd4e34ed5","observation_id":"c8d1d384-004c-4dbe-8987-46750a0b9b7b","resolution":{"observed_at":"2026-05-25T04:35:21.207416Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"cited_work":{"arxiv_id":"2507.02375","doi":null,"metadata_source":"pith","pith_arxiv_id":"2507.02375","snapshot_observed_at":"2026-07-10T08:26:58.960977Z","title":"On discrete gauging and non-invertible selection rules","venue":"hep-th","work_id":"221f546f-a826-47a7-b2a5-a7bdc63284e6","year":2025},"citing_paper":{"arxiv_id":"2605.28141","last_updated":"2026-05-27T08:24:04Z","snapshot_observed_at":"2026-08-13T10:27:17.224836Z","submitted_at":"2026-05-27T08:24:04Z","title":"More about modular symmetries and non-invertible properties in magnetized compactifications","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-06-29T11:26:34.913484Z"},"links":{"cited_paper":"/paper/2507.02375","citing_paper":"/paper/2605.28141"},"observation_digest":"sha256:09b53297831c4a79bc584a56b7b4da07667486e1485c460820e0ef441a76c731","observation_id":"b6860599-50c9-4d69-93f6-a83e22b7420d","resolution":{"observed_at":"2026-06-29T12:53:27.455547Z","resolver_source":"arxiv_id","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"cited_work":{"arxiv_id":"2507.02375","doi":null,"metadata_source":"pith","pith_arxiv_id":"2507.02375","snapshot_observed_at":"2026-07-10T08:26:58.960977Z","title":"On discrete gauging and non-invertible selection rules","venue":"hep-th","work_id":"221f546f-a826-47a7-b2a5-a7bdc63284e6","year":2025},"citing_paper":{"arxiv_id":"2607.08384","last_updated":"2026-07-09T12:03:36Z","snapshot_observed_at":"2026-08-19T21:09:38.805785Z","submitted_at":"2026-07-09T12:03:36Z","title":"Revisiting One-Zero and Two-Zero Neutrino Mass Textures in Light of Recent Oscillation and Cosmological Data","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-07-10T08:20:11.011377Z"},"links":{"cited_paper":"/paper/2507.02375","citing_paper":"/paper/2607.08384"},"observation_digest":"sha256:f3ccc2860b6d158051a51b8a0e937175615e4e60dabf6299cb4a17c5012f7269","observation_id":"02bb63b0-3892-4221-a110-370bb9f9ee98","resolution":{"observed_at":"2026-07-10T08:26:58.962341Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}}],"links":{"evidence":"/evidence","html":"/paper/2507.02375/citation-record","integrity":"/paper/2507.02375/integrity","json":"/paper/2507.02375/citation-record.json","paper":"/paper/2507.02375"},"outbound":[{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:44:23.201861Z","title":"Dijkgraaf, E.P","venue":null,"work_id":"99edc101-a1c9-4df7-9af2-ed55cc06475b","year":1988},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":1,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:21.702255Z"},"links":{"citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:bcae732e8e9cc74f1182a6cc87557a66f1bad6878282d8c039cc0b0108d94c07","observation_id":"ff52e416-5733-4177-8717-2d69f0caba0b","resolution":{"observed_at":"2026-08-06T20:44:23.207031Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"hep-ph/0409098","last_updated":"2004-11-16T17:45:16Z","snapshot_observed_at":"2026-07-07T04:04:53.002745Z","submitted_at":"2004-09-08T19:21:38Z","title":"Searching for realistic 4d string models with a Pati-Salam symmetry -- Orbifold grand unified theories from heterotic string compactification on a Z6 orbifold","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-ph/0409098","snapshot_observed_at":"2026-08-06T20:44:21.800447Z","title":"Kobayashi, S","venue":null,"work_id":null,"year":2005},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":2,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:21.800447Z"},"links":{"cited_paper":"/paper/hep-ph/0409098","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:43d568979b40a825b17525b8beb2fe69270db8c6b7da7375e4ce96d7915bcab6","observation_id":"30f6f163-5a5d-41d2-bf46-d0ae5d35fea7","resolution":{"observed_at":"2026-08-06T20:44:21.800447Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"hep-ph/0611020","last_updated":"2007-01-31T17:38:11Z","snapshot_observed_at":"2026-07-07T04:12:46.643001Z","submitted_at":"2006-11-02T08:03:48Z","title":"Stringy origin of non-Abelian discrete flavor symmetries","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-ph/0611020","snapshot_observed_at":"2026-08-06T20:44:21.936186Z","title":"Kobayashi, H.P","venue":null,"work_id":null,"year":2007},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":3,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:21.936186Z"},"links":{"cited_paper":"/paper/hep-ph/0611020","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:deb6ca905588dd662c45d8ea6f930d746dacab253c0fa7fbbb2e3630744764df","observation_id":"8599c2fb-165c-4685-93db-c3fc27133c28","resolution":{"observed_at":"2026-08-06T20:44:21.936186Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1406.4660","last_updated":"2014-06-18T09:47:04Z","snapshot_observed_at":"2026-08-14T23:29:57.610445Z","submitted_at":"2014-06-18T09:47:04Z","title":"Gauge Origin of Discrete Flavor Symmetries in Heterotic Orbifolds","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1406.4660","snapshot_observed_at":"2026-08-06T20:44:21.971463Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":4,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:21.971463Z"},"links":{"cited_paper":"/paper/1406.4660","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:c66efe300c6d07ff9a57ed0a1fbd332280a84b46162dcb437dd24eae41ba3f17","observation_id":"28e8e730-a085-47a9-a34d-2e3d7db02695","resolution":{"observed_at":"2026-08-06T20:44:21.971463Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2106.12577","last_updated":"2021-06-23T18:00:00Z","snapshot_observed_at":"2026-08-18T23:34:43.753814Z","submitted_at":"2021-06-23T18:00:00Z","title":"Fusion Category Symmetry II: Categoriosities at c = 1 and Beyond","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2106.12577","snapshot_observed_at":"2026-08-06T20:44:21.977515Z","title":"Thorngren and Y","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":5,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:21.977515Z"},"links":{"cited_paper":"/paper/2106.12577","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:31330b79b2b833034ddfbd22b6e131c3d83797b9d6c4ea1f3f9fb4fd8b6c1638","observation_id":"8250c420-9b91-4792-b73c-472980c0fd58","resolution":{"observed_at":"2026-08-06T20:44:21.977515Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.00118","last_updated":"2024-01-31T19:00:04Z","snapshot_observed_at":"2026-08-17T11:04:16.991664Z","submitted_at":"2024-01-31T19:00:04Z","title":"On the Fate of Stringy Non-Invertible Symmetries","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.00118","snapshot_observed_at":"2026-08-06T20:44:21.983024Z","title":"Heckman, J","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":6,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:21.983024Z"},"links":{"cited_paper":"/paper/2402.00118","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:edb469391f3a4950f6d83f35f2cccc3a09207e76c2098cc617c9b5b3ce406264","observation_id":"9062ee79-5d14-4140-9cd8-41e0d34174a2","resolution":{"observed_at":"2026-08-06T20:44:21.983024Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.00105","last_updated":"2024-01-31T19:00:01Z","snapshot_observed_at":"2026-08-16T14:22:45.177540Z","submitted_at":"2024-01-31T19:00:01Z","title":"On a class of selection rules without group actions in field theory and string theory","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.00105","snapshot_observed_at":"2026-08-06T20:44:21.987899Z","title":"Kaidi, Y","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":7,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:21.987899Z"},"links":{"cited_paper":"/paper/2402.00105","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:1e83c59398c3dd369e922028d1be257566bdbd034dc5ebe029be29edbaa61444","observation_id":"aac0c444-bbf5-438e-970c-4433cc8aac29","resolution":{"observed_at":"2026-08-06T20:44:21.987899Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2408.13984","last_updated":"2024-11-26T05:29:17Z","snapshot_observed_at":"2026-08-16T13:23:56.894757Z","submitted_at":"2024-08-26T02:34:40Z","title":"Non-invertible flavor symmetries in magnetized extra dimensions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2408.13984","snapshot_observed_at":"2026-08-06T20:44:21.992600Z","title":"Kobayashi and H","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":8,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:21.992600Z"},"links":{"cited_paper":"/paper/2408.13984","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:6151ad0e3df581c3fb8950702128795badac65e347483fc02f93d0d51fe59c38","observation_id":"0211d646-2a68-495a-af87-dc47918524f4","resolution":{"observed_at":"2026-08-06T20:44:21.992600Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2412.12524","last_updated":"2024-12-17T04:31:27Z","snapshot_observed_at":"2026-08-14T20:30:52.341868Z","submitted_at":"2024-12-17T04:31:27Z","title":"Quantum aspects of non-invertible flavor symmetries in intersecting/magnetized D-brane models","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2412.12524","snapshot_observed_at":"2026-08-06T20:44:21.997608Z","title":"Funakoshi, T","venue":null,"work_id":null,"year":2025},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":9,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:21.997608Z"},"links":{"cited_paper":"/paper/2412.12524","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:25115900743d3b6b80abc08ca523cc6e6b8eaf6919c0e8675359391296f9a00e","observation_id":"57a0f738-3e70-4617-8752-b5c53c84bf3d","resolution":{"observed_at":"2026-08-06T20:44:21.997608Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:44:23.186173Z","title":"Verlinde, Fusion Rules and Modular Transformations in 2D Conformal Field Theory, Nucl","venue":null,"work_id":"f15523f6-e6c7-44e6-baf1-78c0749ea35f","year":1988},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":10,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.002377Z"},"links":{"citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:8c8bd897f4783b4ba049af7e60203436f9ae6d7d739750fa2b04966e24fa2e71","observation_id":"e8ce120c-a7e2-422e-ba4d-e63ded06f7a6","resolution":{"observed_at":"2026-08-06T20:44:23.191065Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:44:23.168225Z","title":"Moore and N","venue":null,"work_id":"a5a936e1-1e31-453f-aa22-d2dd188222cc","year":1989},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":11,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.007082Z"},"links":{"citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:5a19a453f5558aec17755957dcf49688a974f4f9377cacf3ac548a6605804917","observation_id":"a0873002-2102-4c0f-9e54-235ccc798108","resolution":{"observed_at":"2026-08-06T20:44:23.174912Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:44:23.150536Z","title":"Moore and N","venue":null,"work_id":"ca3bdde7-104e-4594-a9d5-6d8df322fa82","year":1989},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":12,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.012119Z"},"links":{"citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:f0e4f24ab1b022275cdebe841dbdbdedaac83ee855064e2143172ead47dd6879","observation_id":"1d42a10a-f6be-4048-bb44-ca380f7c3afe","resolution":{"observed_at":"2026-08-06T20:44:23.155715Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/9306162","last_updated":"1993-07-09T15:56:20Z","snapshot_observed_at":"2026-08-04T16:35:53.525890Z","submitted_at":"1993-06-30T16:28:02Z","title":"Fusion rules in conformal field theory","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/9306162","snapshot_observed_at":"2026-08-06T20:44:22.017295Z","title":"Fuchs, Fusion rules in conformal field theory, Fortsch","venue":null,"work_id":null,"year":1994},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":13,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.017295Z"},"links":{"cited_paper":"/paper/hep-th/9306162","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:12b74f6290869beb1b4a8049cac06f851919c037a4d0e10f5a8d0c7209062c1c","observation_id":"0401cf3b-8148-40fb-8b05-994571958744","resolution":{"observed_at":"2026-08-06T20:44:22.017295Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1704.02330","last_updated":"2017-10-26T16:43:09Z","snapshot_observed_at":"2026-08-15T13:13:56.853592Z","submitted_at":"2017-04-07T18:01:48Z","title":"On finite symmetries and their gauging in two dimensions","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1704.02330","snapshot_observed_at":"2026-08-06T20:44:22.021690Z","title":"Bhardwaj and Y","venue":null,"work_id":null,"year":2018},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":14,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.021690Z"},"links":{"cited_paper":"/paper/1704.02330","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:f00155f46157299ac535d3a7e54c95dce46b9277d516cf17f5bcac82a8995fc2","observation_id":"d00ea535-a1cc-473f-85e1-c6a71c657924","resolution":{"observed_at":"2026-08-06T20:44:22.021690Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2504.09773","last_updated":"2025-09-02T10:18:58Z","snapshot_observed_at":"2026-08-19T21:31:40.291438Z","submitted_at":"2025-04-14T00:28:48Z","title":"Coupling Selection Rules in Heterotic Calabi-Yau Compactifications","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2504.09773","snapshot_observed_at":"2026-08-06T20:44:22.026850Z","title":null,"venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":15,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.026850Z"},"links":{"cited_paper":"/paper/2504.09773","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:c8a629ae44ab3071b79a2287812eb6e1a4360c2d46f9f5110662748e90a8f9fa","observation_id":"3bec23df-7f38-4d79-9137-d73d69fb6b41","resolution":{"observed_at":"2026-08-06T20:44:22.026850Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2305.18296","last_updated":"2023-06-07T01:44:22Z","snapshot_observed_at":"2026-08-10T21:00:13.538331Z","submitted_at":"2023-05-29T17:59:50Z","title":"ICTP Lectures on (Non-)Invertible Generalized Symmetries","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2305.18296","snapshot_observed_at":"2026-08-06T20:44:22.032728Z","title":"Schafer-Nameki, ICTP lectures on (non-)invertible generalized symmetries, Phys","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":16,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.032728Z"},"links":{"cited_paper":"/paper/2305.18296","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:296ef76e22cb931f6f8168762dd18f0cbc85cbe47ee2e9bb507794bfbcae1852","observation_id":"325be6df-cc1e-4852-be71-d584cb27b6bf","resolution":{"observed_at":"2026-08-06T20:44:22.032728Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2308.00747","last_updated":"2024-03-30T04:03:38Z","snapshot_observed_at":"2026-07-06T02:11:23.670680Z","submitted_at":"2023-08-01T18:00:01Z","title":"What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2308.00747","snapshot_observed_at":"2026-08-06T20:44:22.037682Z","title":"Shao, What’s Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries, 2308.00747","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":17,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.037682Z"},"links":{"cited_paper":"/paper/2308.00747","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:20439d335ba5a13ee99d4761ab25b8ce30ba7f160c48ea9bcf66c992e72c2df9","observation_id":"8a08d34d-e555-4ec4-9d81-e0dea80cb685","resolution":{"observed_at":"2026-08-06T20:44:22.037682Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2205.05086","last_updated":"2022-06-02T17:46:11Z","snapshot_observed_at":"2026-08-19T22:09:12.032373Z","submitted_at":"2022-05-10T18:00:00Z","title":"Non-invertible Global Symmetries in the Standard Model","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2205.05086","snapshot_observed_at":"2026-08-06T20:44:22.043711Z","title":"Choi, H.T","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":18,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.043711Z"},"links":{"cited_paper":"/paper/2205.05086","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:8a5bc066f8cd4c0a2284115f08d4ecc8e7b4fd20482b37167112b7775fe900b2","observation_id":"3334ab60-351e-4fa1-9b27-98675c254e43","resolution":{"observed_at":"2026-08-06T20:44:22.043711Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2211.07639","last_updated":"2022-11-14T18:59:59Z","snapshot_observed_at":"2026-08-18T17:18:43.769174Z","submitted_at":"2022-11-14T18:59:59Z","title":"Neutrino Masses from Generalized Symmetry Breaking","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2211.07639","snapshot_observed_at":"2026-08-06T20:44:22.049006Z","title":"Cordova, S","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":19,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.049006Z"},"links":{"cited_paper":"/paper/2211.07639","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:5fb1f92780b263c1fc69a7c79c22b56ed51fe36c44ba36d6cdbdb83f43ba3b82","observation_id":"478ecf53-2102-4364-b694-a2e911cffa78","resolution":{"observed_at":"2026-08-06T20:44:22.049006Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2205.06243","last_updated":"2022-08-03T06:03:29Z","snapshot_observed_at":"2026-08-16T17:00:43.015257Z","submitted_at":"2022-05-12T17:43:52Z","title":"Non-Invertible Chiral Symmetry and Exponential Hierarchies","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2205.06243","snapshot_observed_at":"2026-08-06T20:44:22.054867Z","title":"Cordova and K","venue":null,"work_id":null,"year":2023},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":20,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.054867Z"},"links":{"cited_paper":"/paper/2205.06243","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:d9759f7ff29e51ca85412f12c63060e25d925bb79a41dfcf23d073f0092b7ef0","observation_id":"79098308-f4c4-49ff-be62-f98b2538af44","resolution":{"observed_at":"2026-08-06T20:44:22.054867Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2402.12453","last_updated":"2024-02-19T19:02:06Z","snapshot_observed_at":"2026-08-19T15:34:59.448483Z","submitted_at":"2024-02-19T19:02:06Z","title":"Non-Invertible Peccei-Quinn Symmetry and the Massless Quark Solution to the Strong CP Problem","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2402.12453","snapshot_observed_at":"2026-08-06T20:44:22.060091Z","title":"Cordova, S","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":21,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.060091Z"},"links":{"cited_paper":"/paper/2402.12453","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:4197f9a0a10fb3c2d5357ff1f33c8aca55288ecf6bda6cfd1dbb581b1898d9b4","observation_id":"b440e0c4-39f0-44f3-80eb-28c699857fd2","resolution":{"observed_at":"2026-08-06T20:44:22.060091Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2409.05270","last_updated":"2024-09-09T01:42:12Z","snapshot_observed_at":"2026-08-19T10:38:24.414154Z","submitted_at":"2024-09-09T01:42:12Z","title":"Yukawa textures from non-invertible symmetries","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2409.05270","snapshot_observed_at":"2026-08-06T20:44:22.065956Z","title":"Kobayashi, H","venue":null,"work_id":null,"year":2024},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":22,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.065956Z"},"links":{"cited_paper":"/paper/2409.05270","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:7514caa590e77034c99b85ede173fe08a49d85f79bb418a5e8fd8cae48c92a6e","observation_id":"9dfc7d81-cd47-40ed-9a11-0c78de3eecb1","resolution":{"observed_at":"2026-08-06T20:44:22.065956Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2503.09966","last_updated":"2025-05-24T03:36:20Z","snapshot_observed_at":"2026-08-16T12:50:32.516712Z","submitted_at":"2025-03-13T02:12:48Z","title":"More about quark Yukawa textures from selection rules without group actions","version":3},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2503.09966","snapshot_observed_at":"2026-08-06T20:44:22.070701Z","title":"Kobayashi, Y","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":23,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.070701Z"},"links":{"cited_paper":"/paper/2503.09966","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:9cef390cff4373d8751b59c839bb26e720d82cf6e9cddaf31cc5cc69accd41ca","observation_id":"6c7148c9-52a3-4a45-aaa6-d8d34ea0e026","resolution":{"observed_at":"2026-08-06T20:44:22.070701Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:44:22.075648Z","title":"Suzuki and L.-X","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":24,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.075648Z"},"links":{"citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:17ad93b70b229d4580abcd71e03acec0d70346a1d7d8bf62d70e1a776b8c734f","observation_id":"8fef23f6-b73b-48aa-819a-e310657e1878","resolution":{"observed_at":"2026-08-06T20:44:22.075648Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.05142","last_updated":"2025-05-08T11:26:35Z","snapshot_observed_at":"2026-08-16T03:45:59.838245Z","submitted_at":"2025-05-08T11:26:35Z","title":"Non-invertible symmetry as an axion-less solution to the strong CP problem","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.05142","snapshot_observed_at":"2026-08-06T20:44:22.081660Z","title":"Liang and T.T","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":25,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.081660Z"},"links":{"cited_paper":"/paper/2505.05142","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:8c173e579ac54276e00ae3cd39f02a8d493ea9180780157225389b18d8826aa9","observation_id":"2c28a361-d0c4-4405-8159-87e7e0392023","resolution":{"observed_at":"2026-08-06T20:44:22.081660Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2505.07262","last_updated":"2025-08-27T04:31:29Z","snapshot_observed_at":"2026-08-19T20:17:41.338991Z","submitted_at":"2025-05-12T06:23:05Z","title":"Lepton mass textures from non-invertible multiplication rules","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2505.07262","snapshot_observed_at":"2026-08-06T20:44:22.086840Z","title":"Kobayashi, H","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":26,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.086840Z"},"links":{"cited_paper":"/paper/2505.07262","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:a81d30cb82cfca7b49616c7a9a10212fba1bc706af6d5c599f07d6d451104b47","observation_id":"49934535-da3b-4bd5-8278-ee11dc26ee5c","resolution":{"observed_at":"2026-08-06T20:44:22.086840Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:44:22.092303Z","title":"Kobayashi, H","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":27,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.092303Z"},"links":{"citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:20c7357f448e4e501a227dab75ba5cb96972934b552d58add8e7464f09e2e36d","observation_id":"9efbdd2f-6b7a-4d60-a596-221533ab747f","resolution":{"observed_at":"2026-08-06T20:44:22.092303Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.16706","last_updated":"2025-06-20T02:55:18Z","snapshot_observed_at":"2026-08-19T15:35:19.265482Z","submitted_at":"2025-06-20T02:55:18Z","title":"Radiative lepton seesaw model in a non-invertible fusion rule and gauged $B-L$ symmetry","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.16706","snapshot_observed_at":"2026-08-06T20:44:22.097653Z","title":"Nomura and H","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":28,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.097653Z"},"links":{"cited_paper":"/paper/2506.16706","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:28442b081206d5423679d931f3d14283732cb7f44949c210bccf832c5c9dcdec","observation_id":"235b1a6e-2963-4fcf-8313-3f9887b8a3d4","resolution":{"observed_at":"2026-08-06T20:44:22.097653Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"2506.10241","last_updated":"2025-06-11T23:49:04Z","snapshot_observed_at":"2026-08-14T19:46:26.568661Z","submitted_at":"2025-06-11T23:49:04Z","title":"Matter symmetries in supersymmetric standard models from non-invertible selection rules","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"2506.10241","snapshot_observed_at":"2026-08-06T20:44:22.102376Z","title":"Kobayashi, H","venue":null,"work_id":null,"year":null},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":29,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.102376Z"},"links":{"cited_paper":"/paper/2506.10241","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:da2de310c3bbdf03b5913fe4c0140b9f30df8a823a17d7e6917a7d766a395d4c","observation_id":"466387d3-1235-4e69-8407-e211a9bda2a2","resolution":{"observed_at":"2026-08-06T20:44:22.102376Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0904.2631","last_updated":"2009-04-17T04:34:06Z","snapshot_observed_at":"2026-08-15T05:50:22.299166Z","submitted_at":"2009-04-17T04:34:06Z","title":"Non-Abelian Discrete Flavor Symmetries from Magnetized/Intersecting Brane Models","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0904.2631","snapshot_observed_at":"2026-08-06T20:44:22.107867Z","title":"Abe, K.-S","venue":null,"work_id":null,"year":2009},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":30,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.107867Z"},"links":{"cited_paper":"/paper/0904.2631","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:5c7e26ed075e8ae85b17663d58c7a05ddcc445b4544c9e5e3dc15a1d63ddf7c0","observation_id":"f16e0f20-ee76-4aad-a2c1-c8f0cb8e3d2f","resolution":{"observed_at":"2026-08-06T20:44:22.107867Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1206.2383","last_updated":"2012-08-30T16:45:02Z","snapshot_observed_at":"2026-08-15T00:57:13.297566Z","submitted_at":"2012-06-11T21:33:16Z","title":"Non-Abelian discrete gauge symmetries in 4d string models","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1206.2383","snapshot_observed_at":"2026-08-06T20:44:22.113328Z","title":"Berasaluce-Gonzalez, P.G","venue":null,"work_id":null,"year":2012},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":31,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.113328Z"},"links":{"cited_paper":"/paper/1206.2383","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:a32e016c7ea66dfa53f45bcc62d533df0bb22d2e111e3663d309f846ecf68da9","observation_id":"861bff73-d0b9-4dc0-9dd4-805c0c8dfbeb","resolution":{"observed_at":"2026-08-06T20:44:22.113328Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1306.1284","last_updated":"2013-06-25T03:24:59Z","snapshot_observed_at":"2026-08-15T00:15:02.142294Z","submitted_at":"2013-06-06T02:11:21Z","title":"Discrete flavor symmetries in D-brane models","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1306.1284","snapshot_observed_at":"2026-08-06T20:44:22.118075Z","title":"Marchesano, D","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":32,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.118075Z"},"links":{"cited_paper":"/paper/1306.1284","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:26d2ad0f3e5051049cf9e606964f246cc2b1b0713f34e5962da1c4b2a1a932b3","observation_id":"6af86d19-f3ed-4831-8372-037851f36922","resolution":{"observed_at":"2026-08-06T20:44:22.118075Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0806.4748","last_updated":"2008-09-09T11:31:05Z","snapshot_observed_at":"2026-08-15T10:12:17.467235Z","submitted_at":"2008-06-29T11:31:25Z","title":"Magnetized orbifold models","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"0806.4748","snapshot_observed_at":"2026-08-06T20:44:22.123430Z","title":null,"venue":null,"work_id":null,"year":2008},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":33,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.123430Z"},"links":{"cited_paper":"/paper/0806.4748","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:c1fb2c139420970cff89d1a42a20a46e463eb6d02a9a9eacbf57e8e25e13247a","observation_id":"832ec54c-725b-4534-a4e2-3d05573e18ff","resolution":{"observed_at":"2026-08-06T20:44:22.123430Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1003.3552","last_updated":"2010-04-15T10:15:40Z","snapshot_observed_at":"2026-08-15T05:23:54.581815Z","submitted_at":"2010-03-18T11:30:06Z","title":"Non-Abelian Discrete Symmetries in Particle Physics","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1003.3552","snapshot_observed_at":"2026-08-06T20:44:22.128907Z","title":"Ishimori, T","venue":null,"work_id":null,"year":2010},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":34,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.128907Z"},"links":{"cited_paper":"/paper/1003.3552","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:42625718e1b45ae41215a63b741e3b0bc3cd465cc6731b1e84f6b5a297c76e3e","observation_id":"c0735297-ab04-43aa-9229-0470e2afdf2b","resolution":{"observed_at":"2026-08-06T20:44:22.128907Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:44:22.134408Z","title":"Kobayashi, H","venue":null,"work_id":null,"year":2022},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":35,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.134408Z"},"links":{"citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:b3c016ba278248a59faccb7ee689c8e3cc2bac22ca9e3386e2d867838f7c3fec","observation_id":"c2070782-6368-42a8-8e0c-d5ce867b66f7","resolution":{"observed_at":"2026-08-06T20:44:22.134408Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:44:23.134878Z","title":"Hamidi and C","venue":null,"work_id":"40c9d377-91aa-4fad-af4b-4e223658e3c0","year":1987},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":36,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.139850Z"},"links":{"citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:a771ae2165d9fd5aacdf14aaaff23d32a0283e16a601038bb3ee024578b04aeb","observation_id":"fd8b2e74-be72-49b6-b002-0a79c5ce95db","resolution":{"observed_at":"2026-08-06T20:44:23.139654Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:44:23.118690Z","title":"Dixon, D","venue":null,"work_id":"edab6c43-c79b-4bf5-ae06-bc9b3e5d3c96","year":1987},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":37,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.145180Z"},"links":{"citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:c4a98ada806b046bcd389dbd42c5c16185cdd5ed829c8d6c8022c84c49120527","observation_id":"c2362459-86a0-4731-8ed8-b1cdab737552","resolution":{"observed_at":"2026-08-06T20:44:23.123661Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1309.4925","last_updated":"2014-01-24T06:19:16Z","snapshot_observed_at":"2026-08-15T00:02:36.610193Z","submitted_at":"2013-09-19T10:49:54Z","title":"$Z_N$ twisted orbifold models with magnetic flux","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1309.4925","snapshot_observed_at":"2026-08-06T20:44:22.150493Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":38,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.150493Z"},"links":{"cited_paper":"/paper/1309.4925","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:bf4699437c98c5222cb7d9c65eb33c23149677e8861c0a6549389b241d988f7f","observation_id":"d8599d15-0ac7-4b71-a30e-12490289aa21","resolution":{"observed_at":"2026-08-06T20:44:22.150493Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1409.5421","last_updated":"2014-12-23T22:15:04Z","snapshot_observed_at":"2026-08-14T23:18:56.898238Z","submitted_at":"2014-09-18T19:43:19Z","title":"Operator analysis of physical states on magnetized $T^{2}/Z_{N}$ orbifolds","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1409.5421","snapshot_observed_at":"2026-08-06T20:44:22.155241Z","title":null,"venue":null,"work_id":null,"year":2014},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":39,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.155241Z"},"links":{"cited_paper":"/paper/1409.5421","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:384087e496875f92a5f5e2bcbe28661881cb77c917bf631c89ab1f8ae23cad24","observation_id":"e1929542-e0b6-44a6-8f63-b5b8ca4bfc14","resolution":{"observed_at":"2026-08-06T20:44:22.155241Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1709.09784","last_updated":"2017-09-28T02:18:18Z","snapshot_observed_at":"2026-08-14T20:28:55.570991Z","submitted_at":"2017-09-28T02:18:18Z","title":"Zero-modes on orbifolds : magnetized orbifold models by modular transformation","version":1},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1709.09784","snapshot_observed_at":"2026-08-06T20:44:22.160078Z","title":"Kobayashi and S","venue":null,"work_id":null,"year":2017},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":40,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.160078Z"},"links":{"cited_paper":"/paper/1709.09784","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:0f8ee1406ad6578a5aee6208c78f2c0240e146bb6250f4f651540272bdb53ebe","observation_id":"f3c58fca-be5e-426d-b2f8-28d8b88d7317","resolution":{"observed_at":"2026-08-06T20:44:22.160078Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1211.6953","last_updated":"2014-02-03T09:54:13Z","snapshot_observed_at":"2026-08-15T00:37:43.566029Z","submitted_at":"2012-11-29T15:33:11Z","title":"CP and Discrete Flavour Symmetries","version":4},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1211.6953","snapshot_observed_at":"2026-08-06T20:44:22.165307Z","title":"Holthausen, M","venue":null,"work_id":null,"year":2013},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":41,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.165307Z"},"links":{"cited_paper":"/paper/1211.6953","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:b013f131b3f4c2e661daf2f7a062e6b96fc724f44e3cd140ac4b0122b70f5fb0","observation_id":"d9b70fb9-7690-4329-ab6f-12e08d24aad9","resolution":{"observed_at":"2026-08-06T20:44:22.165307Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1502.01829","last_updated":"2015-03-13T15:52:08Z","snapshot_observed_at":"2026-08-17T22:10:01.047282Z","submitted_at":"2015-02-06T09:11:39Z","title":"Symmetries of symmetries and geometrical CP violation","version":2},"cited_work":{"arxiv_id":"1502.01829","doi":null,"metadata_source":"pith","pith_arxiv_id":"1502.01829","snapshot_observed_at":"2026-08-06T20:44:22.376945Z","title":"Symmetries of symmetries and geometrical CP violation","venue":"hep-ph","work_id":"ea88f66c-2051-4ee9-84de-8d406dced33b","year":2015},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":42,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.170532Z"},"links":{"cited_paper":"/paper/1502.01829","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:b6fa1b061f0440cccfb9dd5e7246449c2f27232f7ec4c634c428006141920941","observation_id":"00d378aa-aee8-49c0-aa22-f4148b4386db","resolution":{"observed_at":"2026-08-06T20:44:22.382271Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:44:23.102560Z","title":"Krauss and F","venue":null,"work_id":"72b6dc46-fa45-4e45-98ed-889e4968e4d8","year":1989},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":43,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.175763Z"},"links":{"citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:cbba73927d34dd10133437f03d0c2a47014985003c10e0af41169ba699c37c02","observation_id":"cebe8709-d05a-40dc-8464-f2b547429cda","resolution":{"observed_at":"2026-08-06T20:44:23.107710Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":null,"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":"raw_reference","pith_arxiv_id":null,"snapshot_observed_at":"2026-08-06T20:44:23.084860Z","title":"Ibanez and G.G","venue":null,"work_id":"340bbb2f-a029-4eca-9fa8-69dc56dfbb9a","year":1991},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":44,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.180602Z"},"links":{"citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:1a5bc806c2f05ec91617c2cf698b0fc9f5e0d651307ab0a0a3ad0d4887bf0885","observation_id":"bb2fff5c-87aa-4d49-9a42-34ff0d775d5c","resolution":{"observed_at":"2026-08-06T20:44:23.090686Z","resolver_source":"raw_fallback","status":"verified_fuzzy"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"hep-th/9109045","last_updated":"1991-10-02T18:45:00Z","snapshot_observed_at":"2026-07-07T05:00:37.565027Z","submitted_at":"1991-09-24T19:44:00Z","title":"Note on Discrete Gauge Anomalies","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-th/9109045","snapshot_observed_at":"2026-08-06T20:44:22.186196Z","title":"Banks and M","venue":null,"work_id":null,"year":1992},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":45,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.186196Z"},"links":{"cited_paper":"/paper/hep-th/9109045","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:5bd99f3825347e199d5495459120237374dfdaf04dca5fdfb0063d6686f0a60d","observation_id":"b3e2f90d-7a2c-4f47-853f-0619fabfa29e","resolution":{"observed_at":"2026-08-06T20:44:22.186196Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"0805.0207","last_updated":"2008-08-12T08:23:52Z","snapshot_observed_at":"2026-08-15T10:16:25.412288Z","submitted_at":"2008-05-02T10:33:54Z","title":"(Non-)Abelian discrete anomalies","version":2},"cited_work":{"arxiv_id":"0805.0207","doi":null,"metadata_source":"pith","pith_arxiv_id":"0805.0207","snapshot_observed_at":"2026-08-06T20:44:22.339180Z","title":"(Non-)Abelian discrete anomalies","venue":"hep-th","work_id":"363cbba6-d28b-4933-927b-049b2f91503a","year":2008},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":46,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.191362Z"},"links":{"cited_paper":"/paper/0805.0207","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:93cfeff12afbec326b7326dfd50486d73b01cd41834b93ff06b2dad35673a36c","observation_id":"7c0fb26b-a426-4d92-b776-ca2d87c760d7","resolution":{"observed_at":"2026-08-06T20:44:22.344385Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"1504.03470","last_updated":"2015-04-14T09:26:34Z","snapshot_observed_at":"2026-08-14T22:52:32.448084Z","submitted_at":"2015-04-14T09:26:34Z","title":"Anomaly-safe discrete groups","version":1},"cited_work":{"arxiv_id":"1504.03470","doi":null,"metadata_source":"pith","pith_arxiv_id":"1504.03470","snapshot_observed_at":"2026-08-06T20:44:22.317553Z","title":"Anomaly-safe discrete groups","venue":"hep-ph","work_id":"e66de035-a5e1-4fff-bb98-f92b244beef5","year":2015},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":47,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.196431Z"},"links":{"cited_paper":"/paper/1504.03470","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:0a559f827eefae663be6337ce76d148701c659cca0aa3cd4a32c33bbb25042b2","observation_id":"f9e21106-0138-44b1-b740-0c196b0728f0","resolution":{"observed_at":"2026-08-06T20:44:22.322582Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"2111.10811","last_updated":"2022-02-25T09:36:55Z","snapshot_observed_at":"2026-08-20T02:05:47.178015Z","submitted_at":"2021-11-21T12:58:41Z","title":"Anomaly of non-Abelian discrete symmetries","version":2},"cited_work":{"arxiv_id":"2111.10811","doi":null,"metadata_source":"pith","pith_arxiv_id":"2111.10811","snapshot_observed_at":"2026-08-06T20:44:22.292287Z","title":"Anomaly of non-Abelian discrete symmetries","venue":"hep-th","work_id":"a57d883f-8c3a-439a-981f-ede91b507a76","year":2021},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":48,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.202039Z"},"links":{"cited_paper":"/paper/2111.10811","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:444d36f6c41aeb38a9df514d639e27a7fb2055094df81895abffa242bc3ed7ce","observation_id":"b3838891-e43b-4ea9-afff-d03ce1420c00","resolution":{"observed_at":"2026-08-06T20:44:22.299727Z","resolver_source":"local_arxiv","status":"verified_exact"},"standing_notice":{"events":[],"observation":"No event found in the named queried sources as of 2026-08-19T06:32:44.657259+00:00.","reason":null,"source_receipts":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"state":"measured"}},{"citation":{"cited_paper":{"arxiv_id":"hep-ph/0201008","last_updated":"2002-04-26T20:15:27Z","snapshot_observed_at":"2026-08-14T16:14:48.424734Z","submitted_at":"2002-01-02T21:00:06Z","title":"Zeroes of the Neutrino Mass Matrix","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"hep-ph/0201008","snapshot_observed_at":"2026-08-06T20:44:22.207066Z","title":"Frampton, S.L","venue":null,"work_id":null,"year":2002},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":49,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.207066Z"},"links":{"cited_paper":"/paper/hep-ph/0201008","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:5276cccb739317b9ad324285d50970625feb6275cb9584f6a532b90347ae5b78","observation_id":"1a79701d-105e-429a-ac1b-ccef6903b04c","resolution":{"observed_at":"2026-08-06T20:44:22.207066Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}},{"citation":{"cited_paper":{"arxiv_id":"1108.4534","last_updated":"2011-09-07T22:49:11Z","snapshot_observed_at":"2026-08-15T04:37:33.990814Z","submitted_at":"2011-08-23T09:32:25Z","title":"Two-zero Textures of the Majorana Neutrino Mass Matrix and Current Experimental Tests","version":2},"cited_work":{"arxiv_id":null,"doi":null,"metadata_source":null,"pith_arxiv_id":"1108.4534","snapshot_observed_at":"2026-08-06T20:44:22.212392Z","title":"Fritzsch, Z.-z","venue":null,"work_id":null,"year":2011},"citing_paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules","version":1},"reference_index":50,"source":"pdf_text","source_observed_at":"2026-08-06T20:44:22.212392Z"},"links":{"cited_paper":"/paper/1108.4534","citing_paper":"/paper/2507.02375"},"observation_digest":"sha256:1db074efe9592e3ddba16be5a3c5957bbdf8b5512f6322e5f60c6a25de71b5a1","observation_id":"b244d80f-c24d-45e6-8112-5bd1d763e690","resolution":{"observed_at":"2026-08-06T20:44:22.212392Z","resolver_source":null,"status":"unresolved"},"standing_notice":{"events":[],"reason":"canonical_work_link_unavailable","source_receipts":[],"state":"unavailable"}}],"paper":{"arxiv_id":"2507.02375","last_updated":"2025-07-03T07:15:03Z","latest_version":1,"primary_category":"hep-th","snapshot_observed_at":"2026-08-15T21:15:10.333070Z","submitted_at":"2025-07-03T07:15:03Z","title":"On discrete gauging and non-invertible selection rules"},"reference_resolution":{"displayed":50,"state_counts":{"malformed_identifier":0,"metadata_mismatch":0,"parse_uncertain":0,"unresolved":38,"verified_exact":4,"verified_fuzzy":8},"total_outbound_references":50},"refusal":"A citation records a reference. It does not transfer a finding from one paper to another.","schema":"pith.paper-citation-record.v1","standing_sources":[{"observed_at":"2026-08-19T06:32:44.657259+00:00","source":"crossref"},{"observed_at":"2026-08-19T06:32:39.956319+00:00","source":"retraction_watch"}],"thesis":"As of 20 August 2026, this Paper Citation Record lists 50 of 50 outbound references and 14 inbound Pith citation observations for arXiv:2507.02375."}